(a nice one from three years ago)
"A statistical treasure, it is" ..... Yoda
The first point of the game is unique - it always has the same two posts, in the same positions. We know that #1 and #2 should be mirror images in the statistics, since one will always win and the other will sit down. To the extent that they're not, we have statistical opportunities to probe. One or the other will always end Round 1 with ZERO points. But, how do we deal with this?
On average, #1 will serve once more per game than #2. So, by separating Singles and Doubles games, we can compute the relative advantage of serving/receiving in Singles/Doubles by looking at the relative performance of #1 and #2 (after correcting for player ratings, of course). The same applies, at a rapidly decreasing extent, to #3, #4, etc.
By studying a particular player's performance in post #1 (let's say in Singles) and comparing against ALL post #1 performances, we can also measure the relative effectiveness of his serve, even vis-à-vis individual opponents. Of course, a large historical database is needed.
OK, guys, what else can we learn from this unique situation?